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Simplifying 45 = 4(5 + -8n) + 7(-7 + -6n) 45 = (5 * 4 + -8n * 4) + 7(-7 + -6n) 45 = (20 + -32n) + 7(-7 + -6n) 45 = 20 + -32n + (-7 * 7 + -6n * 7) 45 = 20 + -32n + (-49 + -42n) Reorder the terms: 45 = 20 + -49 + -32n + -42n Combine like terms: 20 + -49 = -29 45 = -29 + -32n + -42n Combine like terms: -32n + -42n = -74n 45 = -29 + -74n Solving 45 = -29 + -74n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '74n' to each side of the equation. 45 + 74n = -29 + -74n + 74n Combine like terms: -74n + 74n = 0 45 + 74n = -29 + 0 45 + 74n = -29 Add '-45' to each side of the equation. 45 + -45 + 74n = -29 + -45 Combine like terms: 45 + -45 = 0 0 + 74n = -29 + -45 74n = -29 + -45 Combine like terms: -29 + -45 = -74 74n = -74 Divide each side by '74'. n = -1 Simplifying n = -1
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